[FOM] Question concerning Poincare, intuitionism, and problem solving

[Steve Stevenson]

Several mathematicians, notably Poincare, Hadamard, and Polya,  
contributed a great deal to the understanding of problem solving. In  
the *Foundations of Science*, Poincare' said ``It is by logic that we  
prove, but by intuition that we discover."  Intuition is what ``goes  
on in the very soul of the mathematician."

I have a PhD student studying problem solving and the question comes  
up "How influenced was Poincare' (and the others) by what was going  
on around them? And in turn, how much were they influenced?" Dewey  
was certainly writing on problem solving at the same time. Alan  
Newell (Turing award winner) said he became a "student of Polya" to  
gain insights.

I'd appreciate any pointers that one has on this interaction of  
mathematics and psychology in this area.
--
steve
steve at cs.clemson.edu
also fatmarauder at gmail.com

“The surest way to become a pacifist is to join the infantry.” Bill  
Mauldin